Proof Writing & Problem Solving · Superchallenge problem

Let $F_1 = P_1$ and, for $k \ge 2$, $F_k = (F_{k-1} \Rightarrow P_k)$, so for example $F_3 = \big((P_1 \Rightarrow P_2) \Rightarrow P_3\big)$. In how many of the $2^{10}$ truth assignments to $P_1, P_2, \ldots, P_{10}$ is $F_{10}$ true?